An organ pipe 1.00m long is initially open at both ends and resonates at a fundamental frequency f1 when sounded at room temperature where the speed of sound is v=340ms−1. One end of the pipe is then fitted with a movable piston so that the pipe can be made closed at that end while its other end remains open.
(i) Write the expressions for the frequencies of the harmonics produced when the pipe is (a) open at both ends and (b) open at one end only.
(ii) Keeping the air temperature unchanged, determine how far the piston must be moved inward so that the pipe, now closed at one end, again resonates at the same frequency f1.
(iii) Calculate the lowest frequency greater than f1 that can be produced by both the fully open pipe and the pipe closed at one end. State the corresponding harmonic numbers in each configuration.